Stitz-Zeager_College_Algebra_e-book

However hls1 also contains the points 0829 3 6 3

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Unformatted text preview: of the phrase ‘King George III’ were part of George’s name. The next hurdle to overcome is the description of HLS1 itself − a variable and some seemingly extraneous punctuation have found their way into our nice little roster notation! The way to make sense of the construction {(x, 3) : −2 ≤ x ≤ 4} is to verbalize the set braces {} as ‘the set of’ and the colon : as ‘such that’. In words, {(x, 3) : −2 ≤ x ≤ 4} is: ‘the set of points (x, 3) such that −2 ≤ x ≤ 4.’ The purpose of the variable x in this case is to describe inﬁnitely many points. All of these points have the same y -coordinate, 3, but the x-coordinate is allowed to vary between −2 and 4, inclusive. Some of the points which belong to HLS1 include some friendly points like: (−2, 3), (−1, 3), (0, 3), (1, 3), (2, 3), (3, 3), and √ 5 (4, 3). However, HLS1 also contains the points (0.829, 3), − 6 , 3 , ( π, 3), and so on. It is impossible to list all of these points, which is why the variable...
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